The sum of the squares of two consecutive positive numbers is 85?

Let the numbers be m & m+1 (consecutive)

Hence their squares are

m^2 & ( m + 1)^2 => m^2 & m^2 + 2m + 2

Hence

Their sum is

m^2 + m^2 + 2m + 1 = 85

2m^2 + 2m - 84 = 0

m^2 + m - 42 =0

Factor

(m + 7)(m - 6) = 0

Hence the numbers are 6 & 7 .